# Induction, magnetism (flux), and current

candybish
Hi,

inductance is the property of a conductor by which a change in current in the conductor "induces" (creates) a voltage (electromotive force) in both the conductor itself (self-inductance). --wikipedia

From what I understand, the inducing happens due to the resulting change in magnetic field from the change in current

Also, from what I understand, the greater the current, the greater the magnetic field.

However, the inductance of a coil is not dependent on the current. My reasoning behind that is that for every unit of current in the coil, there is a unit of magnetic field which induces an opposing voltage (and in turn current) which is proportional. So if current increases, a proportional amount of opposing current will be there, therefore it cancels out in the formula just like this guy explains:
watch?v=Ab0dJLdmApg

Let me know if I understand everything so far because now my real question comes:

Self induction of a coil is constant. But what if you have a changing magnetic field coming from an external source. Is it possible that the external flux of the magnetic field superimposes with the flux coming from the coil itself to give a net flux of zero? This would mean inductance would be zero and the coil would behave like a straight wire with little or no inductance.

In school I was taught that inductance of a given coil cannot change which is why this question is really bugging me.

Thanks

Gold Member
candybish
See http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indcur.html

The "inductance" is a constant related to the material and its geometry.
It tells you what the reaction will be for a certain change in current.

You seem to be mixing up the two ideas based on the similarity of the names.

Which two ideas? inductance and magnetic field of a coil?
Okay then maybe I should use the term reactance?

For instance, if you measure the inductance of the primary of a transformer, you will measure let's say 1 H. Then when you short the secondary, you will measure something like 0.001 H on the primary. The inductance value goes down or "reactance" goes down. I was explained the reasoning behind this using equivalent circuits of transformers but an equivalent circuit does not show what is actually happening, just an equivalent representation.

Intuitively I see the current of the primary being hit with the magnetic field of the primary AND secondary and because of this, the flux cancels out and the current can travel through the coil without being opposed by a net flux as it would in a single coil.

So if it isn't called inductance, I think I understand why, BUT is what I am explaining correct about what happens to the current and the magnetic fields from primary and secondary?

Thanks

mikeph
I think everything should make sense to you once you begin using the concept of a inductance matrix rather than a single value. When you have more than one alternating currents in a region where the EM fields can interact, the concept of a single inductance per component doesn't have a whole lot of use.

Rather than thinking about L as in V = L(dI/dt), you have to think of a matrix L_ij where V_i = L_ij*(dI_j/dt). i.e. the Inductance I_ij is the ratio of the voltage over the ith component to the time derivative of the current over the jth component. This is essential in situations where the whole point is to couple the circuits (e.g. a transformer).

L_ij = L_ji so in your two inductor setup, you have three different inductances: the self-inductances of each coil (which can be calculated in the absence of disturbances), plus the off-diagonal mutual inductance between the coils.